The moving sum (MOSUM) procedure has been adopted
in simultaneously testing for and localising multiple change points
[1]}, [2]}, [3]}.
For the canonical segmentation problem it scans the data for change points
using the statistics \(\mathcal {T}_{s, k, e}(X)\)  over a fixed grid \((s, k, e) \in \mathcal {S}_{\text{M}}(G)\) ,
which is fully determined by the choice of a bandwidth \(G = G_n\)  as
\(\mathcal {S}_{\text{M}}(G) = \left\lbrace (s, k, e): \, s = k - G, \, e = k + G, \, k = G ,\ldots , n - G\right\rbrace .\) 
